Smectic A phases of strongly polar molecules

The first evidence that more than one form of smectic A exists came from an observation of Sigaud et of a phase transition that was detected by calorimetry, but could not be observed optically. X-ray studies revealed that this was a transition between two forms of the A phase the higher temperature phase was characterized by a pair of refiexions corresponding to a layer spacing and the lower temperature one by two pairs of reflexions corresponding to fi / and 21 respectively. The former type of smectic A is called the monolayer (A ) phase and the latter the bilayer (Aj) phase. A third type which has a layer spacing intermediate between / and 21, has been identified and is called the partially bilayer (A ) phase. The structures of these phases are represented schematically in fig. 5.6.1. 

and later Prost and Barois, developed a phenomenological theory of the A phases in which the free energy density is expressed in terms of two coupled order parameters, p r) describing the mass density wave, and 4 r), the dipolar density wave arising from the antiparallel associations of neighbouring molecules. The total free energy is written as 

Barois, Frost and Lubensky have used the phenomenological model, within the framework of the mean field theory, to construct phase diagrams involving the polymorphic forms of the A phase. They have predicted three kinds of critical points, the A -Aj critical point, the Aj-A tricritical point and the A, N-A bicritical point, the salient features of which are summarized below. 

Since A and Aj have the same symmetry, it is to be expected that a first order A -A2 phase boundary should terminate at a critical point. This has been confirmed in a binary liquid crystal system. Flots of wavevectors against temperature for different concentrations (A ) in the vicinity of the critical point are shown in fig. 5.6.3. It is seen that the first order A -A transition manifests itself as a jump in the wavevector, accompanied by a two-phase coexistence region. On increasing X the magnitude of the jump as well as the width of the two-phase region decrease, until finally only a 

The transition between the Aj and Aj phases can be of first or second order because of the exact doubling of the layer periodicity (see Landau and Lifshitz, p. 468). Thus the Aj-Aj phase boundary - say in a binary 

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